PRICING SUPPLEMENT NO. 3                                        Rule 424(b)(3)
DATED:  May 19, 2003+                                      File No. 333-104455
        May 20, 2003++
(To Prospectus dated April 24, 2003,
and Prospectus Supplement dated April 24, 2003)

                                 $10,227,293,162
                         THE BEAR STEARNS COMPANIES INC.
                           MEDIUM-TERM NOTES, SERIES B

Principal Amount: $325,000,000   Floating Rate Notes [x]  Book Entry Notes [x]


Original Issue Date: 5/22/2003   Fixed Rate Notes [ ]     Certificated Notes [ ]


Maturity Date: 5/23/2005         CUSIP#: 073928ZK2

Option to Extend Maturity:       No    [x]
                                 Yes   [ ]  Final Maturity Date:


                                              Optional            Optional
                         Redemption           Repayment           Repayment
   Redeemable On          Price(s)             Date(s)            Price(s)
   -------------       --------------       -------------      -----------
        N/A                  N/A                 N/A                 N/A

Applicable Only to Fixed Rate Notes:
-----------------------------------

Interest Rate:

Interest Payment Dates:

Applicable Only to Floating Rate Notes:
--------------------------------------

Interest Rate Basis:                     Maximum Interest Rate:  N/A

[ ]  Commercial Paper Rate               Minimum Interest Rate:  N/A

[ ]  Federal Funds Effective Rate

[x]  Federal Funds Open Rate             Interest Reset Date(s):  Daily

[ ]  Treasury Rate                       Interest Reset Period:  Daily

[ ]  LIBOR Reuters                       Interest Payment Date(s):  *

[ ]  LIBOR Telerate

[ ]  Prime Rate

[ ]  CMT Rate

Initial Interest Rate: 1.5%              Interest Payment Period:  Quarterly

Index Maturity:  N/A

Spread (plus or minus):  + 0.25%

+  $175,000,000 was traded on May 19, 2003.
++ $150,000,000 was traded on May 20, 2003.

*  8/22/03, 11/22/03, 2/22/04, 5/22/04, 8/22/04, 11/22/04, 2/22/05 and 5/23/05.

The distribution of Notes will conform to the requirements set forth in Rule
2720 of the NASD Conduct Rules.